Lemma  suggests that the subgraph densities of induced subnetworks of a network is sufficient for estimating the kernel function \(f\)  from a network sample. In particular, [1]} showed that for a graph \(G \sim \mathcal {G}(n, f)\) , that the moments of subgraph counts from \(G\)  are moments of the kernel function \(f\) . Specifically, we have the following Lemma:
